"Computation of Multivariate Normal and t Probabilities" by Alan Genz and Frank Bretz is an introductory yet comprehensive book on the numerical evaluation of the multivariate normal (MVN) integral. The book is small, with 126 pages, and is part of Springer's Lecture Notes in Statistics series. The topic is important and relevant, as the normal distribution is central to multivariate analysis and has a long-standing historical significance. However, the integral of the MVN density function does not have a closed-form solution, posing a challenge for statisticians. Modern computers have largely mitigated this issue, but numerical integration remains difficult in high dimensions. The book is well-structured, readable, and written by knowledgeable authors. It provides an overview of mathematical relations, identities, and expressions useful for evaluating the MVN integral. While the text is rich in references, the results are discussed briefly, and relationships between them are not thoroughly explored. The authors aim to give readers a glimpse into the subject rather than a comprehensive reference. The book includes discussions on approximations of the integral using inequalities, series expansions, and reparametrizations, as well as numerical integration techniques. However, the technical nature of the subject and the brief discussion may pose difficulties for readers without prior familiarity with these topics. The authors provide software implementations in R and MATLAB, which are presented as subsections of the book. The functions are described with references to relevant sections of the book, and examples of how to call them are provided. However, the presentation of the software has an unpolished feel, and its integration with the rest of the book could be improved. The strengths of the book include its readability, well-structured content, comprehensive bibliography, and clear mathematical notation. It serves as a good introduction and bibliographical review for readers with some prior knowledge of the subject. The authors are knowledgeable, and it is hoped they will publish a more thorough treatment of the subject in the future."Computation of Multivariate Normal and t Probabilities" by Alan Genz and Frank Bretz is an introductory yet comprehensive book on the numerical evaluation of the multivariate normal (MVN) integral. The book is small, with 126 pages, and is part of Springer's Lecture Notes in Statistics series. The topic is important and relevant, as the normal distribution is central to multivariate analysis and has a long-standing historical significance. However, the integral of the MVN density function does not have a closed-form solution, posing a challenge for statisticians. Modern computers have largely mitigated this issue, but numerical integration remains difficult in high dimensions. The book is well-structured, readable, and written by knowledgeable authors. It provides an overview of mathematical relations, identities, and expressions useful for evaluating the MVN integral. While the text is rich in references, the results are discussed briefly, and relationships between them are not thoroughly explored. The authors aim to give readers a glimpse into the subject rather than a comprehensive reference. The book includes discussions on approximations of the integral using inequalities, series expansions, and reparametrizations, as well as numerical integration techniques. However, the technical nature of the subject and the brief discussion may pose difficulties for readers without prior familiarity with these topics. The authors provide software implementations in R and MATLAB, which are presented as subsections of the book. The functions are described with references to relevant sections of the book, and examples of how to call them are provided. However, the presentation of the software has an unpolished feel, and its integration with the rest of the book could be improved. The strengths of the book include its readability, well-structured content, comprehensive bibliography, and clear mathematical notation. It serves as a good introduction and bibliographical review for readers with some prior knowledge of the subject. The authors are knowledgeable, and it is hoped they will publish a more thorough treatment of the subject in the future.